{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# pomegranate / hmmlearn comparison\n",
    "\n",
    "<a href=\"https://github.com/hmmlearn/hmmlearn\">hmmlearn</a> is a Python module for hidden markov models with a scikit-learn like API. It was originally present in scikit-learn until its removal due to structural learning not meshing well with the API of many other classical machine learning algorithms. Here is a table highlighting some of the similarities and differences between the two packages.\n",
    "\n",
    "<table>\n",
    "<tr>\n",
    "<th>Feature</th>\n",
    "<th>pomegranate</th>\n",
    "<th>hmmlearn</th>\n",
    "</tr>\n",
    "<tr>\n",
    "<th>Graph Structure</th>\n",
    "<th></th>\n",
    "<th></th>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>Silent States</td>\n",
    "<td>&#10003;</td>\n",
    "<td></td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>Optional Explicit End State</td>\n",
    "<td>&#10003;</td>\n",
    "<td></td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>Sparse Implementation</td>\n",
    "<td>&#10003;</td>\n",
    "<td></td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>Arbitrary Emissions Allowed on States</td>\n",
    "<td>&#10003;</td>\n",
    "<td></td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>Discrete/Gaussian/GMM Emissions</td>\n",
    "<td>&#10003;</td>\n",
    "<td>&#10003;</td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>Large Library of Other Emissions</td>\n",
    "<td>&#10003;</td>\n",
    "<td></td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>Build Model from Matrices</td>\n",
    "<td>&#10003;</td>\n",
    "<td>&#10003;</td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>Build Model Node-by-Node</td>\n",
    "<td>&#10003;</td>\n",
    "<td></td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>Serialize to JSON</td>\n",
    "<td>&#10003;</td>\n",
    "<td></td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>Serialize using Pickle/Joblib</td>\n",
    "<td></td>\n",
    "<td>&#10003;</td>\n",
    "</tr>\n",
    "<tr>\n",
    "<th>Algorithms</th>\n",
    "<th></th>\n",
    "<th></th>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>Priors</td>\n",
    "<td></td>\n",
    "<td>&#10003;</td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>Sampling</td>\n",
    "<td>&#10003;</td>\n",
    "<td>&#10003;</td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>Log Probability Scoring</td>\n",
    "<td>&#10003;</td>\n",
    "<td>&#10003;</td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>Forward-Backward Emissions</td>\n",
    "<td>&#10003;</td>\n",
    "<td>&#10003;</td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>Forward-Backward Transitions</td>\n",
    "<td>&#10003;</td>\n",
    "<td></td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>Viterbi Decoding</td>\n",
    "<td>&#10003;</td>\n",
    "<td>&#10003;</td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>MAP Decoding</td>\n",
    "<td>&#10003;</td>\n",
    "<td>&#10003;</td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>Baum-Welch Training</td>\n",
    "<td>&#10003;</td>\n",
    "<td>&#10003;</td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>Viterbi Training</td>\n",
    "<td>&#10003;</td>\n",
    "<td></td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>Labeled Training</td>\n",
    "<td>&#10003;</td>\n",
    "<td></td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>Tied Emissions</td>\n",
    "<td>&#10003;</td>\n",
    "<td></td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>Tied Transitions</td>\n",
    "<td>&#10003;</td>\n",
    "<td></td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>Emission Inertia</td>\n",
    "<td>&#10003;</td>\n",
    "<td></td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>Transition Inertia</td>\n",
    "<td>&#10003;</td>\n",
    "<td></td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>Emission Freezing</td>\n",
    "<td>&#10003;</td>\n",
    "<td>&#10003;</td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>Transition Freezing</td>\n",
    "<td>&#10003;</td>\n",
    "<td>&#10003;</td>\n",
    "</tr>\n",
    "<tr>\n",
    "<td>Multi-threaded Training</td>\n",
    "<td>&#10003;</td>\n",
    "<td>Coming Soon</td>\n",
    "</tr>\n",
    "\n",
    "</table>\n",
    "</p>\n",
    "\n",
    "Just because the two features are implemented doesn't speak to how fast they are. Below we investigate how fast the two packages are in different settings the two have implemented. \n",
    "\n",
    "## Fully Connected Graphs with Multivariate Gaussian Emissions\n",
    "\n",
    "Lets look at the sample scoring method, viterbi, and Baum-Welch training for fully connected graphs with multivariate Gaussian emisisons. A fully connected graph is one where all states have connections to all other states. This is a case which pomegranate is expected to do poorly due to its sparse implementation, and hmmlearn should shine due to its vectorized implementations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "import hmmlearn, pomegranate, time, seaborn\n",
    "from hmmlearn.hmm import *\n",
    "from pomegranate import *\n",
    "seaborn.set_style('whitegrid')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both hmmlearn and pomegranate are under active development. Here are the current versions of the two packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "hmmlearn version 0.2.0\n",
      "pomegranate version 0.4.0\n"
     ]
    }
   ],
   "source": [
    "print \"hmmlearn version {}\".format(hmmlearn.__version__)\n",
    "print \"pomegranate version {}\".format(pomegranate.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first should have a function which will randomly generate transition matrices and emissions for the hidden markov model, and randomly generate sequences which fit the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def initialize_components(n_components, n_dims, n_seqs):\n",
    "    \"\"\"\n",
    "    Initialize a transition matrix for a model with a fixed number of components,\n",
    "    for Gaussian emissions with a certain number of dimensions, and a data set\n",
    "    with a certain number of sequences.\n",
    "    \"\"\"\n",
    "    \n",
    "    transmat = numpy.abs(numpy.random.randn(n_components, n_components))\n",
    "    transmat = (transmat.T / transmat.sum( axis=1 )).T\n",
    "\n",
    "    start_probs = numpy.abs( numpy.random.randn(n_components) )\n",
    "    start_probs /= start_probs.sum()\n",
    "\n",
    "    means = numpy.random.randn(n_components, n_dims)\n",
    "    covars = numpy.ones((n_components, n_dims))\n",
    "    \n",
    "    seqs = numpy.zeros((n_seqs, n_components, n_dims))\n",
    "    for i in range(n_seqs):\n",
    "        seqs[i] = means + numpy.random.randn(n_components, n_dims)\n",
    "        \n",
    "    return transmat, start_probs, means, covars, seqs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets create the model in hmmlearn. It's fairly straight forward, only some attributes need to be overridden with the known structure and emissions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def hmmlearn_model(transmat, start_probs, means, covars):\n",
    "    \"\"\"Return a hmmlearn model.\"\"\"\n",
    "\n",
    "    model = GaussianHMM(n_components=transmat.shape[0], covariance_type='diag', n_iter=1, tol=1e-8)\n",
    "    model.startprob_ = start_probs\n",
    "    model.transmat_ = transmat\n",
    "    model.means_ = means\n",
    "    model._covars_ = covars\n",
    "    return model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now lets create the model in pomegranate. Also fairly straightforward. The biggest difference is creating explicit distribution objects rather than passing in vectors, and passing everything into a function instead of overriding attributes. This is done because each state in the graph can be a different distribution and many distributions are supported."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def pomegranate_model(transmat, start_probs, means, covars):\n",
    "    \"\"\"Return a pomegranate model.\"\"\"\n",
    "    \n",
    "    states = [ MultivariateGaussianDistribution( means[i], numpy.eye(means.shape[1]) ) for i in range(transmat.shape[0]) ]\n",
    "    model = HiddenMarkovModel.from_matrix(transmat, states, start_probs, merge='None')\n",
    "    return model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets now compare some algorithm times."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def evaluate_models(n_dims, n_seqs):\n",
    "    hllp, plp = [], []\n",
    "    hlv, pv = [], []\n",
    "    hlm, pm = [], []\n",
    "    hls, ps = [], []\n",
    "    hlt, pt = [], []\n",
    "\n",
    "    for i in range(10, 112, 10):\n",
    "        transmat, start_probs, means, covars, seqs = initialize_components(i, n_dims, n_seqs)\n",
    "        model = hmmlearn_model(transmat, start_probs, means, covars)\n",
    "\n",
    "        tic = time.time()\n",
    "        for seq in seqs:\n",
    "            model.score(seq)\n",
    "        hllp.append( time.time() - tic )\n",
    "\n",
    "        tic = time.time()\n",
    "        for seq in seqs:\n",
    "            model.predict(seq)\n",
    "        hlv.append( time.time() - tic )\n",
    "\n",
    "        tic = time.time()\n",
    "        for seq in seqs:\n",
    "            model.predict_proba(seq)\n",
    "        hlm.append( time.time() - tic )    \n",
    "        \n",
    "        tic = time.time()\n",
    "        model.fit(seqs.reshape(n_seqs*i, n_dims), lengths=[i]*n_seqs)\n",
    "        hlt.append( time.time() - tic )\n",
    "\n",
    "        model = pomegranate_model(transmat, start_probs, means, covars)\n",
    "\n",
    "        tic = time.time()\n",
    "        for seq in seqs:\n",
    "            model.log_probability(seq)\n",
    "        plp.append( time.time() - tic )\n",
    "\n",
    "        tic = time.time()\n",
    "        for seq in seqs:\n",
    "            model.predict(seq)\n",
    "        pv.append( time.time() - tic )\n",
    "\n",
    "        tic = time.time()\n",
    "        for seq in seqs:\n",
    "            model.predict_proba(seq)\n",
    "        pm.append( time.time() - tic )    \n",
    "        \n",
    "        tic = time.time()\n",
    "        model.fit(seqs, max_iterations=1, verbose=False)\n",
    "        pt.append( time.time() - tic )\n",
    "\n",
    "    plt.figure( figsize=(12, 8))\n",
    "    plt.xlabel(\"# Components\", fontsize=12 )\n",
    "    plt.ylabel(\"pomegranate is x times faster\", fontsize=12 )\n",
    "    plt.plot( numpy.array(hllp) / numpy.array(plp), label=\"Log Probability\")\n",
    "    plt.plot( numpy.array(hlv) / numpy.array(pv), label=\"Viterbi\")\n",
    "    plt.plot( numpy.array(hlm) / numpy.array(pm), label=\"Maximum A Posteriori\")\n",
    "    plt.plot( numpy.array(hlt) / numpy.array(pt), label=\"Training\")\n",
    "    plt.xticks( xrange(11), xrange(10, 112, 10), fontsize=12 )\n",
    "    plt.yticks( fontsize=12 )\n",
    "    plt.legend( fontsize=12 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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mkn0xx9bliIiIiIids7tADRAW7EtObh57DqbauhQRERERsXN2GagLjs/TedQi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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f315d8cc9d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "evaluate_models(10, 50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks like in this case pomegranate and hmmlearn are approximately the same for large (>30 components) dense graphs for the forward algorithm (log probability), MAP, and training. However, hmmlearn is significantly faster in terms of calculating the Viterbi path, while pomegranate is faster for smaller (<30 components) graphs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sparse Graphs with Multivariate Gaussian Emissions\n",
    "\n",
    "pomegranate is based off of a sparse implementations and so excels in graphs which are sparse. Lets try a model architecture where each hidden state only has transitions to itself and the next state, but running the same algorithms as last time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def initialize_components(n_components, n_dims, n_seqs):\n",
    "    \"\"\"\n",
    "    Initialize a transition matrix for a model with a fixed number of components,\n",
    "    for Gaussian emissions with a certain number of dimensions, and a data set\n",
    "    with a certain number of sequences.\n",
    "    \"\"\"\n",
    "    \n",
    "    transmat = numpy.zeros((n_components, n_components))\n",
    "    transmat[-1, -1] = 1\n",
    "    for i in range(n_components-1):\n",
    "        transmat[i, i] = 1\n",
    "        transmat[i, i+1] = 1\n",
    "    transmat[ transmat < 0 ] = 0\n",
    "    transmat = (transmat.T / transmat.sum( axis=1 )).T\n",
    "\n",
    "    start_probs = numpy.abs( numpy.random.randn(n_components) )\n",
    "    start_probs /= start_probs.sum()\n",
    "\n",
    "    means = numpy.random.randn(n_components, n_dims)\n",
    "    covars = numpy.ones((n_components, n_dims))\n",
    "    \n",
    "    seqs = numpy.zeros((n_seqs, n_components, n_dims))\n",
    "    for i in range(n_seqs):\n",
    "        seqs[i] = means + numpy.random.randn(n_components, n_dims)\n",
    "        \n",
    "    return transmat, start_probs, means, covars, seqs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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5OEXn4hSdi1PaYpDXJm0kRUVFLF68mLy8PKAheH19PTfccAMrVqygsrKS8vJy\nVqxYwcyZM20RSRxEeWk1x4+V0Cfc75IL7bbk49edkF5emNNOUFVZa+84IiJiZ4899hixsbHExsYS\nGRlJTEwMsbGxxMXFNVtJsiVxcXEUFhZe8DnLli1jxYoVlxtZHIxNRravuuoq7rvvPhYsWIDVasXV\n1ZWXXnqJa6+9loyMDObMmYPBYGDWrFlER0fbIpI4CPOhE4D9pvw7F1NUKLnZJaQdPE7UyN72jiMi\nInb02GOPNf08adIkXnjhBa688spW7yc+Pr7F5yxatKjV+xXHZ5NiG+DWW2/l1ltvPev+3/72t/z2\nt7+1VQxxMObUhmLbXovZnIspMoTN61NITsxVsS0iIk2sViunX+p2++23M3LkSDZu3MhTTz1FWFgY\nS5YsITs7m9raWubPn8+dd94JgMlkYsuWLWRmZrJs2TJGjx7Nxo0bqamp4dlnn+Wqq65i6dKl9O3b\nl3vvvZeYmBjuuecePv74Y3Jzc5k5cyZLliwB4K9//SvLly+nV69ezJ07l7feeotNmzbZ45TIRbBZ\nsS1yJqvVSkZaPu7dXAjp5W3vOE0CQzzxC+jBoeQ8amvrHaK9RUSkK/ny8wMc2HesXY8x9IqeTJk1\n9LL3c+DAAdauXQvAn/70J/r06cNbb71FVlYWcXFxxMbGEhwcjMFgaLbNPffcw6JFi/jHP/7BG2+8\nwT/+8Y+z9r17924++ugj8vLyiImJ4c4776SkpIR//OMfrF+/Hk9PT+6+++5m+xbHY9Op/0ROV1RQ\nQXFRJeEDAzAaHecPhcFgwBQVQm1NfdPKliIiIucyceLEpp8feeQRHn74YQDCwsIIDAwkKysLoNmI\nuIeHB9dffz0AQ4cO5dixc3+waLyOLSgoiMDAQHJzc9m9ezdjxozB398fV1dXbrzxxnZ5XdJ2NLIt\ndmPvJdovxBQVyvav00lOzGXwsBB7xxER6VKmzBraJqPOtuDtfeqb2f3797Ns2TJycnIwGo3k5+dz\nrhmWPT09m352cnLCYrGcc9+nP89gMFBfX09JSUmzYwYHB7fFy5B2pJFtsRtzmuP1azfqFeaDp5c7\nqT/mYqk/9x9BERGR0/3+978nNjaWDRs2sG7dOnx9fdv8GB4eHs1mQWmc6U0cl4ptsQuLxYo57QQ+\nft3w9e9u7zhnMRgNDI4MobKilkzzhadqEhERgYapjocObRiRX7lyJVVVVa2aHvBiREVF8d1333Hy\n5Elqamr3Cw46AAAgAElEQVRYtWpVm+5f2p6KbbGLnKPFVFXWEj4w0GEv7DBFNbSPpCTm2jmJiIg4\ngjPfr868/Zvf/Ib/+Z//Yfbs2VRWVnLLLbfwyCOPkJWV1er3uvMda/jw4cyZM4c5c+Zw5513EhMT\n47Dvo9JAPdtiF+a0hn7tCAfs127Ut78/7t1cSE7MYdqcYfpjJiLSxX311VfNbi9fvrzZ7dtuu43b\nbrut2X2/+93vADh48CDQ0GO9YcOGpsdHjx7ddPuZZ54577FOv7148WIWL14MwJYtW/Dy8rqk1yO2\noZFtsYuMn+bX7ufAxbaTk5FBw4IpKa7iWFaxveOIiIhQWFjImDFjOHbsGFarlXXr1jFixAh7x5IL\nULEtNldbU0eWuZCQnl708HCzd5wLMkU2tJIkJ+XYOYmIiAj4+fmxaNEi7rzzTqZPn05xcTELFy60\ndyy5ALWRiM0dMRdRX28h3AFnITlT/8GBOLsYSUnMZVLcEHvHERER4ZZbbuGWW26xdwy5SBrZFptr\n7Nd2xPm1z+Ti6swAUxAn8srIP15q7zgiIiLSwajYFpszp53AyclIn3A/e0e5KKaoUACSNSuJiIiI\ntJKKbbGpirJqcrKL6d3PF1e3jtHFNHBIEEajgRT1bYuIiEgrqdgWmzqcXgBWiBjk+C0kjbp1d6Xf\nAH+OZRVTXNS2ixOIiIhI56ZiW2wqI7WxX9vxL448XVMrSZJaSUREROTiqdgWmzKnncDN3Zmevb3t\nHaVVBkeGgEF92yIiItI6KrbFZooKyikqqCB8YABGp471q+fp5U7vPr4cySigoqza3nFERESkg+hY\nFY90aOa0hlUjO1oLSSNTVAhWK6T8eNzeUURERKSDULEtNtO4RHtHujjydOrbFhERkdZSsS02YbVY\nMafl4+Xjjl9AD3vHuSR+AT0ICvUkIzWf6qo6e8cRERGRDkDFtthE7rFiKitqiRgYiMFgsHecS2aK\nDKW+zkJ6Sp69o4iIiEgHoGJbbKKxhSS8g7aQNDJFhQBwcL8WuBEREZGWqdgWmzCndcz5tc8U3NML\nH7/upB3Mo66u3t5xRERExMGp2JZ2V1dbz5GMQoJCPfHwdLN3nMtiMBgwRYVQU13XNLuKiIiIyPmo\n2JZ2l3W4iLo6S4cf1W5kimxoJUnRrCQiIiLSAhXb0u4yfmoh6ahT/p2pdz8/eni4kpyUi8VitXcc\nERERcWAqtqXdmVNPYDQa6Bvhb+8obcJoNDA4MoSKshqyDhfaO46IiIg4MBXb0q4qK2o4dvQkvfv5\n4urmbO84baZpgZtEtZKIiIjI+anYlnZ1+FABWDv+LCRnCh8QgJu7M8mJOVitaiURERGRc1OxLe3K\n3Mn6tRs5ORsZOCSY4qJKcrNL7B1HRESkTVgsVqqr6qkor6Gqspaa6jrqauux1Fs0uHSJOs/3+uKQ\nMlJP4OrmTK8wH3tHaXOmqBCSfsgmOSmH0N7e9o4jIiJyyaoqa9mzM5PvtpopLa5i46cbzvk8gwEM\nRgNGowGj0fjTvw2n3Wc4+z6DAaOTAYPRiNEARicjBsNPjzmd9viZ9xmNGIw0HefMY5z/mMYLPu/0\n24afjt3stTTd1zYrXqvYlnZzsrCCwhPlDBoWjNGp832JMsAUhJOzkZTEXK6fbrJ3HBERkVYrLqrg\nu61m9uw8Qk11HS6uTgT3dsfX1wdLvRWL1Yql3orVasVisWKpt2CxgtViabj90z/W036uq7M0u93w\njwWrhYZ/d6AB8hm39rzsfajYlnbTuOhLRCfr127k6uZM/0GBpB44TkF+Gf6BHvaOJCIiclFyjp5k\nx+YMftx3DKvFioeXG9dOHsjIsX04cDCRUaNGtduxrVbrWcW49aei/uz7Gop7i8Vyquhv/BBgaf5B\nwPpTUW/5qag/80PAuT4YNN/u7Meh9rJfr4ptaTcZqT8t0d7J+rVPZ4oKJfXAcZITcxkfM8DecURE\nRM7LarFyKCWPHZvTGyYwAIJCPRk3sT+RV/bCydk230IbDAYMTgaMTjY53GVJSEi47H2o2JZ2YbVY\nMR86gaeXOwFBnXfEd9CwYAxGA8lJKrZFRMQx1dXVk5iQzc4t6eQfLwMaJi4YF92fiEGBGAxt05ss\n56ZiW9rF8dwSKspqGH5V7079P3H3Hq70jfDj8KECSour8PR2t3ckERERoGGti93bM9m1zUx5aTVG\no4Hho3ozNjqCkJ66sN9WVGxLuzCnNvZrd94WkkamyFAOHyogOSmXq8f3s3ccERHp4ooKytm5JYO9\n32dRW1OPm7sz46L7M+bacLx8utk7XpejYlvaRcZP82t3tsVszmVwZAjrP0siOTFHxbaIiNjN0cwi\ndmxO/2nBNfDycSd6+mBGjumDm7uLveN1WSq2pc3V1dVzJKOQwGCPLtFW4e3bjZ5hPmSmF1BZUUO3\n7q72jiQiIl2E1WIl9cBxtm9OJ8tcCEBILy+uiR7AkCtCceqEU+92NCq2pc0dzSyitqae8EGdf1S7\nkSkqhGNZJ0k7cJzhV4XZO46IiHRytbX17N+dxY7NGRSeKAdgwJAgxkX3p19//059vVRHo2Jb2lxj\nv3Z4F+jXbmSKDGFTfDIHE3NVbIuISLspL6vm+28Ps/vbw1SU1+DkZGTE6DDGTuxPUIinvePJOajY\nljaXkXYCg9FAv/7+9o5iMwHBngQEe5CekkdtTR0urvpfS0RE2k5Bfhk7t2Sw7/ss6uosuHdzYcLk\ngYwe3w8Pr87fstmRqSKQNlVVWcuxI0X06uvb5S7GMEWGsO2rQ6Sn5GOKCrV3HBER6eCsVitZ5kJ2\nbE4n5cBxsIKPX3fGToxgxNVhuLqpjOsI9F9J2lRmegFWK0R0oX7tRqaoULZ9dYiDiTkqtkVE5JJZ\nLFaSE3PYsTmd7CMnAejZx4drovtjigrFaFQ/dkeiYlvaVOMS7V1hfu0zhfb2xsvHnbQDedTXW3QF\nuIiItEpNdR17d2Wx85sMThZWgAEGDwtmXHR/wsL9dNFjB6ViW9qUOe0Erm5O9Orra+8oNmcwGDBF\nhbJrq5nDhwroP7jrje6LiEjrlZZU8f02M7u3Z1JVWYuzs5FR4/oydmIE/oEe9o4nl0nFtrSZkpOV\nnMgrY+CQoC47qmuKDGHXVjMpSTkqtkVE5ILyckvZuSWdxIRs6ustdO/hysSpg7hqfD96eLjZO560\nERXb0mYyGqf864L92o36hPvRrbsLyUm5xM6NwqC+OhEROY3VauVwegE7Nqdz6GAeAH4BPRgXHcHw\nq8JwcXGyc0Jpayq2pc2Y07puv3Yjo5ORwZEh7N2VxdEjRYT187N3JBERcQD19RYO7DvGzi0Z5Bwt\nBqBPhB/jJvZn0NBgDc50Yiq2pU1YrVYy0k7Qw9ONwC4+qb4pKpS9u7JITsxVsS0i0sVVV9Wy57sj\nfPdNBiUnqzAYYOgVoYyd2J/eXfD6pq5Ixba0ifzcUspLq4ka2avLXy0dMTAAVzcnUpJymTxzSJc/\nHyIiXVHJyUq+22pmz85MqqvqcHF1YvSEcMZcF46vfw97xxMbUrEtbSIjrXGJ9q7br93I2cWJAaYg\nDuzLIS+3lOBQL3tHEhERG8k9VszOzRkk/ZCNxWKlh6cb11w/gKuu6Uu37q72jid2oGJb2oT5p/m1\nw7twv/bpTFGhHNiXQ3JiroptEZFOzmq1kp6Sz84t6U2TBQQGezAuuj+RI3vh7KyLHrsyFdty2err\nLRxOL8A/sAfevt3sHcchNE5/mJKYw8Spg+wdR0RE2kF9nYWkH7LZsSWdvJxSAPoNCGBcdAQDBgfp\nokcBbFhsf/XVV/zf//0ftbW1+Pj48Nhjj7Fhwwbeffdd/Pz8sFqtGAwGFi1axOTJk20VS9pAdmYR\ntTX1XXKJ9vNxc3chfGAAh5LzKCqowNe/u70jiYhIG6mqrCVhRya7tpopLanCYDQQeWUvxkVHENrb\nx97xxMHYpNg+fvw4S5cu5YMPPiAiIoL33nuPP/zhD4wfP5758+ezcOFCW8SQdnKqX1stJKczRYVw\nKDmP5KQcxk3sb+84IiJymU4WVvDd1gx++O4INdX1uLo5M3ZiBGOuDcfbV4Mqcm42KbZdXFxYtmwZ\nERERAIwaNYqXXnqJ8ePH2+Lw0s7MqfkYDA1fnckpg4eFsObj/SQn5qrYFhHpwI5lnWTH5nQO7M/B\narHi6e3OdVMGM3JsH9y7udg7njg4mxTbfn5+TJgwoen2li1buOKKKwDYvn0727Zto7i4mOjoaBYt\nWoSLi35xO4rqqlqOHjlJzz6++oNzhh6ebvQJ9+OIuZCy0mo8PLX0rohIR2G1WElLzmPH5nQy0wsA\nCO7pxbjo/gy7oidOzkY7J5SOwuYXSO7YsYPly5fzr3/9i8zMTDw8PLjtttuorKzkvvvu48033+T+\n+++3dSy5RJkZhVgt1i69auSFmCJDOJJRSEpSLqPG9bV3HBERaUFdbT37E46yc0sGJ/LKAOg/OJBx\n0f0JHxigtROk1QxWq9Vqq4Nt3LiRp556itdee42hQ4ee9fiXX37Jm2++yYcffnjefSQkJLRnRGml\nHxOKOZxSzthJ/vgHa+T2TBVldXy9Oo/AUDdGX+9v7zgiInIeNdUWMtPKOZxaTk2VBYMRevXrRrjJ\nAy8ffXPblY0aNeqytrfZyPb27dt5+umnefvttwkPDwfgyJEj+Pn54eHhAUBdXR3Ozi1HutwX3Vkk\nJCTY/Vzs+uprXFydiJk6xq7ziDrCuTifgwlbyMstZdjQ4TZptXHkc2FrOhen6FyconNxis4F1FTX\nseWLVL7bmoGl3oqbuzPjYyIYPSEcT293e8ezC/1enNIWg7w2Kbarqqp46KGHeP3115sKbYBXXnkF\nX19fHnnkEaqrq1mxYgXR0dG2iCRtoLS4ivzjZfQ3BWrC/gswRYWSm13CoYN5RI7sZe84IiJCw0I0\nyYm5bPgsiZLiKrp1d+K6KSZGjO6Dm7uWIZG2Y5Pfpq+++oqioiIefPBBgKY5td99910effRRpk2b\nhpOTExMnTmTBggW2iCRtwJzWsGpkhJZovyBTZAib16dwMDFHxbaIiAMoKihn3cokDh3Mw8nJyLVT\nBtLDt4zRYyLsHU06IZsU2zNmzGDGjBnnfOy1116zRQRpB03zaw/SxZEXEhjiiV9ADw4l51FbW4+L\ni74FEBGxh7q6erZ/nc62jWnU1VkIHxhA3I1R+Ad66JowaTf6nkQuidVqxZx6gu4ergSHeNk7jkMz\nGAyYokLY/nU6Gan5DB4WYu9IIiJdTkZqPus+TaQgvxwPTzemzh7GsBE9NbuItDsV23JJTuSVUVpS\n1fCHyqg/VC0xRYWy/et0UhJzVWyLiNhQWUkVX6w+QNIP2RgMMHpCONHTB2ttCLEZFdtyScypDS0k\nEYPUr30xeoX54OHlRsqPuVjqLRidtBiCiEh7slisJGw/zKZ1yVRX1dEzzIe4G6PoGeZj72jSxajY\nlkuS8dPFkeFazOaiGIwGTJGh7N5+mExzIeFa2l5EpN0cyzrJ2o/3k3O0GDd3Z+JujGLk2L4Y9U2s\n2IGKbWk1S72Fw4cK8AvogY9fd3vH6TBMUSHs3n6YlMRcFdsiIu2gqrKWTfHJ7N5xGKwwfFRvJs8a\nioenFl0T+1GxLa2WnXWSmuo6IkZpGrvW6NvfH/duLiQn5jBtzjBdlCMi0kasVitJe7L54vMDlJdW\nExDkQdyNUfTTwIY4ABXb0mrmxin/NL92qzg5GRk0NJj9CUc5llVMrz7qGxQRuVwnjpcS/2kShw+d\nwNnFSEyciXET++PkrGtjxDGo2JZWy0jNBwP0G+Bv7ygdjikqhP0JR0lOylGxLSJyGWpr6ti6MY3t\nm9Ox1FsZODSY6XMi8fVXe6M4FhXb0io11XUczSyiZ28funV3tXecDqf/4ECcXYykJOYyKW6IveOI\niHRIqQeOs35lIicLK/HycWf6nEgGR4aoPU8ckoptaZXMjAIs9VatGnmJXFydGWAKIjkxl/zjpQQG\ne9o7kohIh1FcVMmGVUkkJ+ZiNBoYF92fiVMH4eqmckYcl347pVUyGufXVr/2JTNFhZKcmEtyYq6K\nbRGRi1Bfb+G7b8xs+SKF2pp6+kT4ETcviqBQrWAsjk/FtrSKOS0fZ2cjYf187R2lwxo4JAij0UBK\nUg7XTh5o7zgiIg7tiLmQ+I/3k5dbSvcersTOjeKKq3urZUQ6DBXbctHKSqrIyyklYlAAzi5O9o7T\nYXXr7kq/Af5kpJ6guKgCb19dzCMicqaKsmo2rjnI3u+zABg5tg8xcUPo3kPXC0nH0uK8OC+88IIt\nckgHYD6kKf/aiikqFIDkpFw7JxERcSxWi5U9OzN57bmv2ft9FsE9vVjwq/HMvPkKFdrSIbVYbCcl\nJZGVlWWLLOLgzI392ro48rINjgwBAyQnqtgWEWl0/FgJ/3z1W9Z8tJ/6egtTbxjKLx+4lrB+fvaO\nJnLJWmwj8fT0ZPbs2fTr1w8fn+bzAr/99tvtFkwci9VqJSMtn27dXQjp6W3vOB2ep5c7vfv4ciSj\ngIqyarp7aClhEem6qqvq2PJFCt9tNWO1WBl6RShTZw/Dy7ubvaOJXLYWi+2YmBhiYmJskUUcWOGJ\nckpOVjH0ilAMRl2U0hZMUSEczSwi9cBxRozuY+84IiI2Z7VaObg/hw2rfqS0uApf/+7EzotigCnI\n3tFE2kyLxfbcuXMByM3NpbCwkKFDh7Z7KHE8jVP+qV+77ZiiQtm45iAHE3NVbItIl1N4opx1KxNJ\nT87HycnIdVMGMX7SAFx0Ab50Mi0W20ePHuU3v/kNR44cwc3NjW3btrF48WLi4uKIjo62QURxBOa0\nfAAiBqnYbit+AT0ICvUkIzWf6qo63Nw1OZCIdH51dfVs/zqdbRvTqKuzED4wgLgbo/AP9LB3NJF2\n0eIFkg8++CB3330333//PZ6eDQtw/OpXv+Lll19u93DiGCwWK+a0E/j6d8fXX9PUtSVTZCj1dRbS\nU/LsHUVEpN1lpObztxe2sHl9Cu7dXbhx/kjm3zNWhbZ0ai0OpRUWFhIXFwfQNIF8WFgYtbW17ZtM\nHEbO0ZNUV9UxbERPe0fpdExRIXzzZSoH9+cw9AqdXxHpnEpLqvhy9QGSfsjGYIDR14YTPW0w7t1c\n7B1NpN21WGx7eXmxY8cOxo0b13Tf/v376d5dI5xdRdMS7WohaXPBPb3w8etG2sE86urqcXZWr6KI\ndB4Wi5Xd3x7m6/XJVFfV0bOPDzNujCK0t0/LG4t0Ei0W20uXLuX+++8nJCSEnJwcbrrpJvLz83nl\nlVdskU8cgDktHwzQr7+/vaN0OgaDAVNUKDu3ZGBOO8HAIcH2jiQi0iayj5wk/pP95Bwtxr2bC3E3\nRjFybF+MmtFKupgWi+1Ro0axadMmdu/eTWlpKUFBQVxxxRW4umoVp66gtqaOLHMRob28NRd0OzFF\nhrBzSwYpSbkqtkWkw6uqrGVT/EF278gEKwwf1ZvJs4bi4an3EOmaWiy258+fz7vvvsvEiROb3X/t\ntdeydevWdgsmjiEzo5D6+oarxaV99O7nRw8PV5KTcom7cbhGfUSkQ7JarSTuyebL1T9SXlZDQLAH\ncfOi6DdA7x/StZ232P7ss89YtWoVP/74I3fddVezx0pLSzEaW5zIRDoBc5rm125vRqOBwZEh7Nl5\nhKzDhfSNULuOiHQs+cdLif8kkcz0ApxdjMTEmRg3sT9OzqoVRM5bbMfFxdGvXz8WLlzIrFmzmm/k\n7MyoUaPaPZzYnzk1HydnI30i/OwdpVMzRYWyZ+cRkhNzVWyLSIdRW1PHNxvT2LE5HUu9lUFDg5k+\nNxIfP02iINLovMW2q6srI0aMYNWqVVitVgICGr4G2rFjBwA9e2qass6uvKya3GMl9BsQoBW92ln4\ngADc3J1JScph6g1Dm6bZFBFxVKkHjrN+ZSInCyvx9u3G9DmRDI4MsXcsEYfTYs/2v//9b7Kysnjx\nxRd59dVXWbVqFYGBgWzbto3f//73tsgodnI4rXHKP/XbtTcnZyMDhwST9EM2udklhPb2tnckEZFz\nKi6qYP1nP5KSlIvRaOCa6/tz3ZRBuLppFVyRc2nx/4z4+Hg+//xzLBYL//nPf/jggw/o3bs3M2fO\nVLHdyWWoX9umTFEhJP2QTXJSjoptEXE49fUWvvsmgy1fpFJbU0+fCD/i5kURFOpl72giDq3FYtvV\n1RU3NzcSEhIIDAykb9++APqau5OzWq1kpObj3s1FhZ+NDDAF4eRsJCUxl+unm+wdR0SkSWZGAfGf\nJJKfW0r3Hq7EzYti+FW9VQuIXIQWi+2AgABee+01tm3b1nSh5Pbt2+nRo0e7hxP7KSqooLiokiHD\nQzUVnY24ujnTf1AgqQeOU5Bfhn+gh70jiUgXV15WzcY1B9n3fRYAI8f2YdKMIXTrrrU2RC5Wi3Py\nPPfcc5SXlzN58mTuvvtuANavX8+TTz7Z7uHEfsxp+QCaX9vGTFENFxclJ+baOYmIdGVWi5U9OzN5\n7dmv2fd9FsE9vbjr1xOYefMVKrRFWqnFke3g4GAWL17c7L4nnniC5557DpNJX3V3VhmpjRdHql/b\nlgYNDcZgNJCclMv4mAH2jiMiXVDusWLiP07kaGYRrm5OTJ09jNHj+2F00pzZIpeixWI7JyeH119/\nnaysLCwWCwAVFRXk5uayZMmSdg8otmexWDl86ATevt3w9ddcqbbU3cONvhF+HD5UQGlxFZ7e7vaO\nJCJdRHVVHZs3pLBrmxmrxcrQK0KZOnsYXt7d7B1NpENr8WPq4sWLqa+v54YbbsBsNjNr1iy8vLx4\n/fXXbZFP7CA3u5jKiloiBgbq4hc7MEWGApCcpFYSEWl/VquVA/uO8fpzX/PdNxn4+Hbj1l+O4aY7\nrlKhLdIGWiy28/LyePrpp5k3bx4eHh7cfPPNvPjii7zyyiu2yCd20LREu+bXtovGRSGSE3PsnERE\nOrvy0jree/M7Pl6eQEV5DddNGcS9v49mgCnI3tFEOo0W20icnJzIy8sjKCgIo9FIcXExvr6+HD16\n1Bb5xA4yUn+6OHKAim178PbtRs8wHzLTC6isqNHFSCLSZqxWK4UnyskyF5KZUUhiQh4WS8PiZbHz\nojQLkkg7aLHYXrBgAVOmTCEhIYHrr7+e2267jV69euHtrbmXO6Pa2nqOmAsJ7ulFD083e8fpskxR\nIRzLOknageMMvyrM3nFEpIOy1FvIyS4hy1zAEXMhWeZCystqmh5362Zk5o0jGDqip9oGRdpJi8X2\nzTffzKRJk3B2dmbRokUMHjyYwsJCZs6caYt8YmNZ5kLq6yya8s/OTJEhbIpP5mBiroptEbloNdV1\nHM0saiqsj2YWUVtT3/S4p7c7w0b0pE+4H2ERfhzNTmPYlb3smFik8ztvsT137lxWrlzJnDlz+Oyz\nzwAwGo1NC9tI56Qp/xxDQLAnAcEepKfkUVtTh4tri5+LRaQLKiutbjZqnZNdgtVibXo8MMSzobAO\n96NPuB/evt2ajWBn52g0W6S9nfcdvLy8nPnz55OZmcldd911zue8/fbb7RZM7MOclo/RyUCfcD97\nR+nyTJEhbPvqEOkp+ZiiQu0dR0TsrLHf+khGQ2F9xFxI4YnypseNTgZ69fFpKq7D+vnRvYeu+RCx\nt/MW2//4xz9ISEjg8OHDGs3uIirKa8jJLqZvhD+ubhpJtTdTVCjbvjpEcmKuim2RLqi+3kLuaf3W\nR8yFVJzeb+3uzABTUNOodc8+Pri4ONkxsYicy3krqrCwMMLCwujXrx8jRoywZSaxk8OHToBVS7Q7\nitDe3nj5uJN64Dj19RactHqbSKd2er/1kYxCso9cuN86KMQLo1FtICKOrsXhSxXaXUfj/Nrq13YM\nBoMBU1Qou7aaOXyogP6D9d9FpDMpK6ki63BDYX3EXEjusdb1W4tIx6BeAWmSkZqPm7szPXtrWkdH\nYYoMYddWMylJOSq2RTqw0/utGy9mPF+/dZ8If8L6+WqOfZFOQsW2AFBUUEFRQQWDI0Mwql3BYfQJ\n96NbdxeSk3KJnRuFQV8Zi3QIDf3WxU2F9QX7rSP86BmmfmuRzqrFYjs9PZ3Nmzdz9913k5qayh//\n+EeMRiMPP/wwQ4cOtUVGsQFzWsOqkRHq13YoRicjg4eFsPf7LI4eKSKsn2aJEXFE1VUN/daNhfV5\n+60j/OkT7kdgiKf6rUW6iBaL7aVLl3L33XcD8MQTT3DdddcRGRnJE088wQcffNDuAcU2Gvu1w9Wv\n7XBMw0PZ+30WyYm5KrZFHERZSVWzUevz9Vs39lyr31qk62qx2C4tLWXatGkUFBSQnJzMO++8g7Oz\nM3/+859tkU9swGqxYk47gZe3O/6BPewdR84QMTAAVzcnUpJymTxziN6wRWzMarVSkF/eVFgfySig\nqKCi6fFT/db+9InwU7+1iDTTYrFtMBiorKxk7dq1jB8/HmdnZ2pra6mpqWlpU+kgjueUUFFewxVX\nh6mQc0DOLk4MMAVxYF8OebmlBId62TuSSKd2er/1kYxCsg6fo996SFDTqLX6rUXkQlostm+99VYm\nTpyIwWDgX//6FwAPPvggkydPbvdwYhtNS7SrX9thmSJDObAvh+TEXBXbIm2ssd/6iLmALHMhRzOL\nqKu1ND3u5e1O5JW9mqbgU7+1iLRGi8X2/PnzmTt3Lm5ubjg7Nzz9f/7nfxg0aFC7hxPbyEhtuDhS\ni9k4roFDg3ByMpKSmMPEqfp/T+RyVFXWc2Dfsaae69zsYqyn2q0JCvFsKqzDwv3w8etuv7Ai0uFd\n1NR/u3fv5osvvqCqqooXX3yRvLw8wsLC6NatW3vnk3ZWV1vPEXMBQSGeeHi52zuOnIebuwvhAwM4\nlJxHUUEFvv568xdprfKyatZ8tJ+UpOPAcQCcnIz07utLmPqtRaSdtFhs/+1vf2PDhg3Mnj2bf//7\n38hUW1cAACAASURBVAAkJiayatUqnn/++Ys+0FdffcX//d//UVtbi4+PD48//jgDBgzghRdeYOPG\njRiNRiZPnsyiRYsu/dVIq2X99HVp+CCNajs6U1QIh5LzSE7KYdzE/vaOI9KhpB08zuoV+ygvrcbH\n34WRY/oTFu5HrzAfnNVvLSLtqMXVSz788EPee+89/vu//xsXFxcA7r33XpKSki76IMePH2fp0qUs\nW7aMtWvXMmPGDB599FHi4+PZvXs3a9asYdWqVezatYsvvvji0l+NtJq5qYVEU/45usHDQsAAyYm5\n9o4i0mHU1taz7tNE3n9rF1UVtUyZNZRrpgYwYdJA+kb4q9AWkXbXYrHt7Ozc1KvdOFOF9fTmtovg\n4uLCsmXLiIiIAGDUqFEcOnSI9evXM3fuXJydnXFxceGGG25g/fr1rX0Nchky0k5gNBroG+Fv7yjS\ngh6ebvQJ9yPrcCFlpdX2jiPi8HKzi3nzpW/4/tvDBP5/9u47vqoyXfT4b5f0XkgnPSGQAkloASnS\nQpEiCAooOjNWrIB37lXnzpxzZ+4Zj9eG7ehYxuOICKiAIiQ0qQGEBEgCpPfeC+nZe98/EoIIuIGU\nnfJ8P598SNZea68ni2Tn2e963ud1tuQPL9xF1HQ/6bokhOhTepPtKVOm8Pjjj7N//36am5s5fPgw\nzz77LHfdddctn8Te3v6a/Q8fPszo0aPJycnB09Oza7unpydZWVm3+S2IO9XU2Epxfg0e3naYmN5S\n+b4wsKAQF9BB2gUZ3RbiZnRaHXE/ZfDJxqNUlF5m/BQfHl03FRc3G0OHJoQYgvQm23/84x+JjIzk\no48+wsjIiE8++YRx48bxxz/+8Y5OeOLECb744gteeuklmpqaMDa+OhHF1NSUpqamO3pecftyMyvR\n6aSEZCAJCnUF4FJSsYEjEaJ/qq1u4l8fnWD/rkuYmxuz6rEJzF0SIn2whRAGo9Ddbk1IN+zfv5//\n+3//L++//z6jRo1i0aJFvPTSS0RFRQFw9OhR3nzzTbZv337T54iPj++rcAe95NM15KY3EjXbEfth\nMvt+oDi6p5z62jZmL3XByFjv+2Uhhoyi3CaSfq6hvU2Hs4cpoeNtMDGVJFsI0T2RkZHdOl5v7cDh\nw4f5+OOPKSsrQ6PRXPPYgQMHbvlEcXFx/Md//AefffYZPj4+APj6+pKbm9uVbOfm5uLnp7/LQne/\n6cEiPj6+W9fi5L6DGJuomTF7AirVwE7aunstBpKGqjQOxaRiaeJGSIT7dY8PpWuhj1yLqwbztWhp\nbmPPd8kkxldjZKzinuXBhE/wvGlt9mC+FrdLrsVVci2ukmtxVU8M8upNtv/0pz/x5JNPEhgYiFJ5\nZwlZc3MzL7/8Mh988EFXog0wb948PvroIxYvXoxWq2XLli1s2LDhjs4hbk9tdSOV5Q0EjnIe8In2\nUBMU4sKhmFRSkotvmGwLMZTkZVex46sEaqqacBtuy72rw3EYZmnosIQQooveZNvJyYnVq1d36yQH\nDhygurqaF198EejoZqJQKPjyyy+5cOECS5YsQaFQsHDhQqZPn96tc4lbk53esUS79NceeIa5WGHv\naEH6pTLa2jRSiyqGJI1Gy5G9aRw7kA7AlFkBTJ0TKIMHQoh+R2+y/eyzz/LXv/6VqVOnYm5+7ap1\n48aNu6WTLFiwgAULFtzwsfXr18tCNgaQldaRbPvK5MgBR6FQEBTqQtxPmWSllXf03xZiCKksv8z2\nTWcpyq/B1t6MJSvD8ZT2pUKIfkpvsr17925iYmI4dOgQKtXVETSFQkFsbGyvBid6h06nIzu9HEtr\nExyd5XbrQBQU6krcT5mkJpVIsi2GDJ1Ox9lTecTuvEBbq4awsR7MXRKCqZmRoUMTQoib0ptsx8XF\nceTIEWxtbfsiHtEHykrqabjcSlikhyzuMEC5D7fF0tqE1AslaDValHLrXAxyjZdb+GHreVIvlGJq\nZsSih8YQPMbN0GEJIYReepPtkJCQ214xUvRvWVeWaJd67QFLoVQQFOLCmbhccrOr8PGX/0sxeGWk\nlPH91+e4XN+Ct78Dix8Ix8bOzNBhCSHELdGbbLu4uLB06VLCw8OxsLC45rG//vWvvRaY6D3ZnfXa\nPgGSoA1kQaGunInLJTWpRJJtMSi1tWk4sOsSPx/LRqlSMOuekURN80OhlDtyQoiBQ2+y7ejoyLJl\ny/oiFtEHNO1acrMqcXS2xNpGRoYGMi8/B0zNjEhJKiZ6SbCUBIlBpaSolu2bzlJeUo+jsyVLV0fg\n4i7LrQshBh69yfYzzzzTF3GIPlKQW01bq0a6kAwCKpWSwFHOJMYXUJRfi7unzKsQA59Oq+PE4Sx+\n2pOCRqNl3GRvZi0cJS0uhRAD1k2T7UcffZRPPvmEOXPm3HTETLqRDDxZ6VKvPZgEhbqQGF9ASnKx\nJNtiwKuraWLH5nPkZFRgYWXCovtHEzDS2dBhCSFEt9w02X7uuecA+Nvf/tZnwYjel51WgUKpwNtP\netIOBn4jhqE2UpKaVMLM+SMNHY4Qd+zi+SJ2bUukuamNwGBnFq4YjYWliaHDEkKIbrtpsh0WFgbA\nli1beOONN657fPny5Wzbtq33IhM9rrmpjcL8Gtw9bTExlb60g4GRsRr/ICdSkkooL61nmLOVoUMS\n4ra0NLcRsz2Z82cKUBspWXBfKBETvWQOghBi0Lhpsn3w4EEOHjzI0aNH+d//+39f81hdXR15eXm9\nHpzoWbmZlei0OqnXHmSCQlxISSohJalEkm0xoORnV7H9q7PUVDXiNtyGJasicHSShbaEEIPLTZPt\n0aNH09TUxP79+3F2vrZmzt3dnUcffbTXgxM9Kzu9s+Wf1GsPKgGjnFEqFaQmFzNlVoChwxFCL41G\ny5F9aRzbn44OuGumP9OiR6CSxZmEEIPQTZNtBwcHFixYgI+PD6NGjerLmEQvyUovx8hYhYennaFD\nET3IzNwYb38HstIqqK1uNHQ4QvymqooGtm9KoDCvBhs7M5asCsfLV+aQCCEGL72t//pjot3S3CY1\nx7eprraJitLL+I90QqWW0aPBJijUlay0ClKSS1CbGzoaIa6n0+k493M+MTuSaWvVEBrpzrx7QzE1\nk9dyIcTgNiCzrg9fP0xORoWhwxhQrpSQ+MqqkYPSiGAXAFKSSgwciRDXa7zcwrb/PsMPW8+jVCpY\n+mAE966KkERbCDEk6B3ZvhmdTmew2eJ1NU188V8nmDDFhxkLRspiB7ega4n2QJkcORhZ2Zji4WVH\nXlYlgaOlL7HoPzJTy9j59Tku17Xg5efAkpVjsLGT2y9CiKFD78j2Cy+8QGVl5TXbUlJSWLFiRa8F\npc/vnr0Lh2EWnDqazT/eOExhXrXBYhkIdDodWenlWFga4+Qi3SoGq6BQF3Q6KC1sMXQoQtDepiF2\nRzKb/nGKxoZWZi4YyUNPRkmiLYQYcvQm20FBQSxbtoxt27bR1NTEa6+9xlNPPcVDDz3UF/HdkIeX\nHY+vn8qEqT5Uljfw2bvHO5b2bdcaLKb+rLz0MpfrWvAJGCa9awexoFBXAErymwwciRjqSovq+OTt\no5w6mo2jkyV/eO4uJs/wR6mU1x8hxNCjN9l+8skn2bJlCzExMUyaNIm6ujp27drFokWL+iK+mzIy\nVhO9OIQ1T0VhbWPK0f3pfLrxKKXFdQaNqz/KTutYot1XWv4NavaOFji5WlFR0kJNlXQlEX1Pp9Vx\n4nAmn7x9lLKSesZO8uaxdVNw9bA1dGhCCGEwepPtpqYmvvrqKwoKClizZg0nTpxg165dfRHbLfH2\nd+TJF6cRPt6TkqI6Pn7rCMcOpKPV6gwdWr+RdaW/tixmM+iNHjccrRY+fP0QPx/Llt8D0Wfqapv4\n8h8n2ff9RUzN1Dzwh/HMXxaKkfEdTw0SQohBQW+yPX/+fJqamti+fTvr1q1j8+bNHD9+nGXLlvVF\nfLfExNSIhfeP5oE/jMfc3JiDu1P4/L3jVJZfNnRoBqfRaMnNrMBhmAU2dmaGDkf0solTfQmbaItS\nqSRmezKfv3ecspJ6Q4clBrlLiUV89PphstMrCBjpxJMvTidwlEzUFUIIuIVuJO+88w6hoaFdXzs5\nOfHOO+9w+PDhXg3sTgSOcubJ/zGdPd8lceFcEf948wizFoxk7CRvFEO0VrAwr4bWFg2+0oVkSFAo\nFAz3NWfW3PHE7kju/D04zF0zA7hrpj9qtXTuET2npbmdmB3JnD+dj9pIyfxloURGecncECGE+AW9\nyfYvE+1fmjZtWo8H0xPMLYxZ9lAkQSEu7P4uiT3bk0lJLmHR/WOG5MjulXptH+mvPaRYWpmw7KFI\nQiLc2fNtEkf2pnHxfBELl49muI+9ocMTg0B+ThU7vjpLdWUjrh423LsqHEdn6XYkhBC/NmiL6YLD\n3fH0c2DX1vOkXyrjw9cPMXdJCGFjPYbUqEtWegUKRUdtuxh6RgS74O3nwMHdKZyOy+Gf7x9n3CRv\nZswPklVYxR3RarQc2Z/O0f3p6HQ6Js/0Z/qcEbIyrRBC3MSgTbYBrKxNeeAP4zn3cz6xOy+w8+tz\npCQVs2D5aCytTAwdXq9raW6nMLcat+G2slLbEGZiasS8paEEh7uza9t5Th/PITW5hPn3hUldrbgt\nVRUNbN+UQGFeDTZ2ZixZGY6Xn4OhwxJCiH5Nb7Kt0WhIT08nKCiItrY2duzYgUKhYPHixRgZ9f8E\nTqFQED7BE58AR3Z+fY7UC6Xk5xxiwX2hjAxzM3R4vSo3qxKtVierRgoAPH3seXz9VI4dyODYgXS+\n/vRngse4Eb0kZEi8+RR3TqfTce7nfGJ2JNPWqiEk3J35y0LlTbwQQtwCvff9/v3f/50tW7YA8Oqr\nr/LNN99w4sQJ/vznP/d6cD3J1t6cNU9GEb0kmNaWdrb9dzzffZlAU2OroUPrNdnpnf21pV5bdFKr\nVUyPHsHj66fh7mXHhXNFfPCfP3Hu5zx0OmkTKK7X2NDKtv8+ww9bz6NUKrh3dThLH4yQRFsIIW6R\n3pHtEydOEBsbS2trK99//z0//vgjTk5OzJ8/vy/i61EKpYIJU3zxG+HEjs1nST5bSG5mJQvvH41/\nkJOhw+tx2WkVqI2UeHjbGToU0c84uVjxu2cmcyYuh4O7L/H9lvMkJRSy4L4w7B0tDB2e6CcyU8v5\n/utz1Nc14+lrz5KV4djay3LrQghxO/SObBsZGaFUKjl9+jQ+Pj44OXUkpQN5FMzRyZLfPzOZu+cF\n0dDQwlcfn+LHbxJpbWk3dGg95nJdM2Ul9Xj5Oki7N3FDSqWC8Xf58NT/mI7/SCey0yv48PVDxP2U\niVajNXR4woDa2zTE7kxm0z9O0nC5hRnzg1jz1CRJtIUQ4g7oHdn29fXl5Zdf5ty5czzyyCMAfPvt\ntwwbNrDrgJUqJVNmBRAwyokdX50l/kQumanlLF45Bi/fgT/hJ1tWjRS3yMbOnJV/GM+Fc0XE7Ehm\n/66LXDhXyD3LR+PqYWPo8EQfKy2uY/umBMqK63EYZsG9qyNwGy7LrQshxJ3Sm2y/9tprbN++nalT\npzJ37lwASktL+fvf/97rwfUFFzcbHn1hCof3phF3MIP//iCOiVN9mTEvCLXRwB0RvrJEu2+g1GsL\n/RQKBSHh7vgGDmPf9xc4f6aATzYeJWqaL9OiR2A0gH8XxK3RaXWcOpbNgR8voWnXEhnlxeyFozA2\nGdRNq4QQotfd9FW0qqoKe3t76uvrmTVrFtCRZAP9aqn2nqBWq5g5fySBo5zZufkcJw9nkZFSxpKV\n4QNyREen05GVVo65hTHOrtaGDkcMIOYWxixeGU5IhAc/fpNI3E+ZXEos5p7lo2VhpEGsvraZnV+f\nJSutAnNLYxauGM2IYBdDhyWEEIPCTZPtBx98kN27dzNt2jQUCsV1NdoKhYJLly71eoB9abh3R2u0\nAz9e4vTxHD595xhTZgYwZXYAKtXAWbChsuwy9bXNBI9xG7LL1Ivu8RsxjCdfnMah2FROHcniXx+e\nYMz44cxeOAozc2NDhyd60KXEYnZtO09TYxv+I51YdP8YaQUphBA96KbJ9u7duwFISUnps2D6A2MT\nNfOWhjIixIXvt5zjyL400i+VsnhlOE4uA2Mp4qslJFKvLe6csYmaOYuCCQl354et5zn3cz7pl8qY\nd28II8Nch9RKrINRa0s7MTuSOfdzPmq1knlLQxk7yUv+X4UQoocNnOHaPuYbOIwnX5zOmHHDKS6o\n5eO3jnR0adD2/y4s2Wkd/bXltr/oCW7DbXn0hSnMmB9Ec1Mb33wRz5Z/nqaupsnQoYk7VJBbzUdv\nHObcz/m4uFvz2PqpjJvsLYm2EEL0Apn58htMzYxY9MAYRoS4sOubRPbvukjqhRIWPzCm3/Yi1mq0\n5GRWYu9oIW26RI9RqZTcNTOAkWGu7NqWSNqFUnIyKpl1z0giJ3pJudIAodVoOXoggyP70tDpdEy6\n25+7545ApZZxFyGE6C3yCnsLRoS48NSL0xgZ5kp+dhUfvXGYM3E5/bLXeFFBLS3N7TKqLXqFwzBL\n1jwVxcIVo1EoYPe3SXz+/nEqSusNHZrQo/FyO5+/H8fh2FSsrE1Y82QUs+4ZKYm2EEL0slt6ldVq\ntZw5c4b9+/cD0Nzc3KtB9UfmlibctyaSpasjUKmU7P42iU3/ONXvbqVndZaQSMs/0VsUCgXhEzxZ\n+z/v7ngDmlPNR28c4ci+NDTtshhOf1NV0cDh2FSO7C6nILea4DFuPLFhGt7+8hohhBB9QW8ZSXJy\nMmvXrsXe3p6qqipmzZrFK6+8wqRJkwZdC0B9FAoFIRHuePk58P3Wc2SmlPNf/+8Q85aGEhrh3i/q\nHbPTK0CB/CEVvc7K2pTlD48lJamYPd8lcygmlQvnili4YjQeXnaGDm9Ia7jcwoVzRSQlFFKYWw2A\n2kjBklXh/ea1Sgghhgq9yfbLL7/Mxo0bCQ8PZ968eQC88sorrFmzZsgl21dY2Ziy6tEJnD2Vx97v\nL7Djq7OkJBWz4L4wLCwN1zKrtaWd/Jwq3DxspD2b6DNBoa54+zty4MdLxJ/I5bN3jzH+Lh9mzAuS\nBVH6UFtrO6nJpSQmFJCZWo5Oq0Oh6LjLFRrpQXN7CWGRHoYOUwghhhy9fwlbWloIDw8H6BoNsbe3\nR6PR9G5k/ZxCoSBiohc+AcPY+fVZUpJKyMuu4p77wggKdTVITHnZVWg1OlmiXfQ5UzMjFtwXRki4\nO7u2nefno9mkJpcwf1koASOdDR3eoKXVaMnOqCApvpBLScW0tXa8Lrt62BAa4U5wuDtW1qYAxMeX\nGTJUIYQYsvQm205OTnz33XcsXbq0a1tsbCyOjlKmAGDnYM7DT03i1NEsDuxOYevnZwgb68HcJSGY\nmhn1aSxZ0vJPGJiXnwNPbJjG0f3pHD+YweZPfiYk3J3oJcEGveszmOh0OooLaklKKCD5bBEN9S0A\n2NqbERrhQWiEO47OA2NNACGEGAr0Jtt/+ctfePrpp3n11VdpbGwkKioKFxcX3njjjb6Ib0BQKBVM\nnOaHX5ATOzefJfFMATnpFSy8fwx+I/pulDk7vQK1Womnj32fnVOIX1Mbqbh7XhCjxrjxw9bzJJ8t\nJDO1jOjFwYRGeki98B2qrmwgKaGQpPgCKssbADAzN2LsJC9CIzzw8LaTayuEEP2Q3mTb29ubmJgY\nMjMzqa+vx8nJCXd3d0pKSvoivgFlmLMVv3v2Lo4fzODI3jQ2/eMkYyd5MeueUb1eu9pQ30JpUR0+\nAY6ojVS9ei4hboWzqzW/f/Yufj6WzU97Utix+RyJ8YUsuC8MOwfpAX8rGi+3cOF8MUnxBRRcmeio\nVjJqtBuhke74j3CS1n1CCNHP6c0AFy1axO7du/H39+/aptVquffeezlx4kSvBjcQqVRKps4OJGCk\nEzs2n+NMXC6ZqeUsXhneqyPO2RmyRLvof5RKBROn+hIU4sKP3ySSmVrOh68f4u65Ixg/xRelLIZz\nnbbWdlIvlJKUUEhmSlnHqrWKjvKw0AgPRoa5YGLatyVqQggh7txNk+1t27bxySefUFRURHR09DWP\nNTQ0YG8vpQq/xdXDlsfWTeFQTCpxhzL5/P3jTJrux/ToEb0y8iz12qI/s7U3Z9VjE0hOKCRmRzJ7\nv79I8tmONoHObtaGDs/gtFod2ekVJCcUcCmpmNaWjomOLu7WhEZ4EBzuhrWNmYGjFEIIcSdummwv\nX76c6dOns3LlSv76179ee5BaTVBQUK8HN9Cp1Spm3TOKwGAXdm4+S9xPmaRfKmPJynBcPWx67Dw6\nnY6stHLMzI1wde+55xWiJykUCkIjPfAdMYy9318gKb6Qj986wqS7/Zg6O3DIlT/pdDpKCmtJjC/k\nwrlCLtd1THS0sTNj/F3uhEZ4MMxFJjoKIcRA95tlJMOGDetaNfLXnnvuOd55551eCWqw8fSx54kN\n09i/6xJn4nL4dONRps4J5K4Z/ihV3a+3rKpooK6mmVGjXVHIbXnRz1lYmnDvqghCIzz48ZtEjh3I\n4FJiMQuWh+HtN/jvzFRXNpJ8toCk+EIqyi4DHa0TI6O8CI1wZ7i3vfweCyHEIKK3ZjslJYXXXnuN\n/Px8tNqOpZibmpqwspIRl9thbKJm/rJQRoQ48/2W8xyKSSXtQimLV45hWDfbdGWnd9RrS39tMZD4\nBznx1P+Yzk8xKZw6ms0XH5wgYqIns+4Z1edtM3tbY0MrF88XkRRfQH5Ox0RHlVrJqNGuhEZ44B8k\nEx2FEGKw0ptsv/LKK8yYMYPHH3+cl19+mb/97W9s376dRx55pA/CG3z8RnQkGDHbk0mML+Afbx5h\nxvwgJk7xvePRrCv12r6Bg39UUAwuxiZqoheHEDzGnV1bz5NwMo+0i6XMXxpqsMWhekpbm4a0C6Uk\nJRSQkVKGVtMx0dHb35GwSHeCQl0H3ZsKIYQQ19ObbDc0NPD0008DYGJiwqRJkwgPD+fRRx9l06ZN\nvR7gYGRqZsSSVeEEhbqw65tE9n1/kdTkEhY/EH7bLdG0Wh05GZXY2ptj52DRSxEL0bs8vOx4bN1U\n4g5lcGRvOls/P0NQqAvz7g3FysbU0OHdso7fxwqSEgq5lFhMa0s7AM5uHRMdQyJkoqMQQgw1epNt\nIyMjEhMTCQsLw8jIiOLiYlxcXKTPdg8ICnVluLc9P36bSEpSCR+9cYg5i4IJn+B5y4tTFBfU0tzU\nxqjRA3sUUAiVWsmUWYGMDHVl1zcdvxPZ6RXMXjiK8PGe/baOuWOiYx1JCQVcOFtEfV0z0DHRcdxk\nb0Ij3HFylY4rQggxVOlNtl944QUee+wx4uLiWLJkCcuWLcPBwQFvb+8+CG/ws7AyYfnDY0lKKGTP\nd0ns2taRZCxcMfqWRvSy06+0/JN6bTE4ODpb8fBTk0g4lcv+XZfYtS2RpIRC7lkehsMwS0OH16Wm\nqpHksx0rOpaXXp3oGDHRk9AIDzx9ZKKjEEKIW0i2Z86cSVxcHCqVit///veEh4dTWVnJ1KlT+yK+\nIUGhUBAW6YG3nwPfbzlPRkoZ//X/DjF/aSjB4W6/OcqdldY5OdLfoa/CFaLXKZQKIqO8CRjlzJ5v\nk0i9UMqHrx9m6uxAJt3th6oHuvjciabGzomOCYXkZVUBHQtZjQxzJTTCHf+RTqjVQ6uFoRBCiN92\nS2uIJyYmUlxcjEaj6doWGxvLwoULb/lE7e3tvP7663z++eccPnwYZ2dn3nvvPb788kvs7e3R6XQo\nFArWr1/PrFmzbv87GQSsbc1Y/fgE4k/ksu+Hi3y3KYGU5GLmLw3F3NLkuv017Vrys6twcbe+4eNC\nDHTWNmas+N04UpKK2fNdMj/tSeHiuSLuWTEad0/bPomhvU1D2sVSkuILSP/FREcvPwfCIj0YGSYT\nHYUQQtyc3mR7w4YNnDx5Em9vb5TKq6NJCoXitpLttWvXEhYWdt0o7YMPPsgzzzxzGyEPbgqFgrGT\nvPENHMbOr89x8XwxuVlV3LM8jBHBLtfsW1XeikajlRISMagpFApGhrnh7e/I/l2XOHsqj8/eOcqE\nqb5Mjx6BscktjRncFp1WR05WJUnxBVxKLKaluXOio6s1IRHuhIS7Y2MnEx2FEELop/ev1OnTp9m/\nfz9mZt37w/L0008zevRo3nvvvW49z1Bh72jBw2sncfJwFj/tSWHLZ6cZPW440YuDu0bRKkpaAWn5\nJ4YGM3NjFq4YTUiEOz9uS+Tk4SxSkoqZvywM/yCnbj+/TqejtLiOpPhCks8WUl/bMdHR2saUyChv\nQiPdcZaJjkIIIW6T3mTbw8MDlar7NYijR4++4fa4uDiOHTtGbW0t06dPZ/369RgZyS1ZAKVSwaS7\n/fAf6cTOzWc5fzqfnIwKFt0/Bp8ARypKWlCplHj62Bs6VCH6jI+/I0+8OI0je9OIO5TJVx+fIizS\ngzmLgzG3ML7t56utbiQpoZDkhELKSuoBMDFVEz7Bk9AId7x8HWSioxBCiDumN9meM2cOjz32GNHR\n0detGnk7ZSQ3MmrUKCwtLVm9ejVNTU089dRTfPzxx6xdu7ZbzzvYOLlY8fvn7uLo/nSO7k/nXx92\nrLRXV92Gt78DRsY9fxtdiP7MyEjFzAUjCR7jxg9bz5MYX0BGahnRi4MJCXfX2zqzqbGVS4nFJMYX\nXDPRMSjUhdAIDwJGOqE2komOQgghuk+h0+l0v7XDQw89dOMDFQq++OKL2z5hUFBQ1wTJX9u3bx8f\nf/wxW7duvenx8fHxt33OwaSmspXzJ2q4XNdRQzpitBX+wd1b7l2IgUyr1ZGT2kBqYj1ajY5hriaE\njLfB3OLaN6EajY6yomYKs5soL2pGq+3Ybu9kjLu3Ga6eZhgZy5LpQgghrhUZGdmt4/UOif7rX/+6\n4fazZ89268QAeXl52NvbY2nZ0Tu3vb0dtVr/KG13v+mBburdGn7ak0JifC6z54/D3lFWjoyP+oyn\newAAIABJREFUjx/yPxdXDMVrMW4cVFc2sGtbItnpFRzbU8mM+UEoTasYZudNUkIhF88XdU10HOZi\nRWiEO6ER7tjY3d6qrQPVUPy5uBm5FlfJtbhKrsVVci2u6olB3luqP0hISCA/P58rg+ANDQ28++67\nnDx5slsn37hxI3Z2dvzpT3+ipaWFLVu2MH369G4951BgZKRizqJgHNybJdEWopOdgwUPPjGRxDMF\nxO68QOyOC6jUCjTtxQBY2ZgSMdGra6Ljra7SKoQQQnSH3mT7P//zP9m+fTsBAQEkJycTFBREbm4u\nzz333C2fpLKykgcffBDoKD9Zs2YNKpWKTz/9lL/97W9ER0ejUqmYNm0av/vd7+78uxFCDGkKhYLR\n44bjF+TE3p0XSE8pJjTCg9BID7x8HVDKREchhBB9TG+yvW/fPvbt24eVlRXz5s1j8+bNHD9+nDNn\nztzySRwcHNizZ88NH3v//fdvPVohhLgFllYmLH0wovNW6BhDhyOEEGII0zsbSK1Wd3Uh0XbOKJo8\neTL79+/v3ciEEEIIIYQY4PQm20FBQTzxxBO0t7fj4+PDW2+9RUxMDPX19X0RnxBCCCGE6AOVtU1s\n3Z/Gj6er2XMih5TcKppb2g0d1oCnt4zk1VdfZfPmzajVal566SX+z//5Pxw5coSXXnqpL+ITQggh\nhBC9RKPVcTa1jJgTOZy+VIpW29EM43T6eQAUCnBztMDHzQZfdxt83GzwcbPG3tpUJprfIr3J9uHD\nh7smLXp5efHpp5/2elBCCCGEEKL3VNQ0se/nPPaeyqWipgkAPw8boid601ZfjLmtG9lFdWQV1ZJd\nVMex80UcO1/Udby1hTG+bjZ4u1l3JeEeTpaoVbJewa/pTbY/+OADZsyYIUuoCyGEEEIMYBqNlvjU\nMmJP5HLmUglaHZiZqJgb5U30BC/8h9sCEB9fSWSkV9dxOp2O8uomsotqySqqI7uoluyiWs6ll3Mu\nvbxrP7VKiZerFT6uNvi4W3eOgttgaTa0c0i9yXZUVBTLly8nKioKGxubax578skney0wIYQQQgjR\nfWXVjez/OY99p3KpqG0GIGC4LdETvZka7o6ZyW+ngwqFAid7c5zszZkQ4tq1vbG5jeyu5LtjFDyv\nuI7Mglo4ffV4JzuzrsTbtzMJd7Y3HzJlKHqT7draWkaOHElNTQ01NTV9EZMQQgghhOgGjUbL6Uul\nxJ7MJSGltHMUW828SR2j2H4ett0+h7mpEcG+DgT7Olxz3sLyy9cl4aculHDqQskvjlV3JOCu1vi4\nd9SBe7pYY2Kk6nZc/Y3eZPvvf/97X8QhhBBCCCG6qayqkb2nctn3cx5VdR2j2CM87Yie6MWUMe6Y\n6hnF7i6VSomnS0fiPC3Co2t7dV3zL2rAOz4uZVdyIauyax+lUoH7MEt8OydhXknC7axMezXm3qb3\nij/00EM3HOZXKBRYW1szZswYHnzwQUxMTHolQCGEEEIIcXPtGi2nL5Z0jGKnlqHTdYwcL5jsQ/RE\nL3zcbPQ/SS+zszbFztqUiCCnrm0tbRpyi+u6RsGzCmvJKa4jv7Sew2d/cayVSUfi7Xp1MqbbMEtU\nA2RVYL3J9tSpU9m+fTsLFizA2dmZ8vJy9uzZw/z587GysmLfvn1kZGTICLgQQgghRB8qqWxg76lc\n9v+cR3V9CwBBXnZET/TmrjFumBr37ih2d5kYqQj0tCPQ065rm1aro7SqsXMyZi05naPhCSllJKSU\nde1nbKTCy8WqI/nuLEXxdrXG3LT/TcbU+79w6NAhNm/efM3kyNWrV/P888/zz3/+k/vvv58FCxb0\napBCCCGEEKJjFPvUhRJiT+RwLr0cnQ4szIy45y4foid64+1qbegQu0WpVODqaIGrowWTwty6tl9u\nbL06At5ZC55dVEt6/rXzCV0dLLo6oVxpTTjM1sygkzH1Jtu5ubnXlYiYmJiQm5sLQGNjIxqNpnei\nE0IIIYQQFFd0jmKfzqOmcxR7lI890RO9mTzabVBOLPwlS3NjQv0dCfV37NrW1q6loKz+F5Mxa8kq\nrCMusZi4xOKrx5oZdUzGdLfurAe3YbizFUbqvukJrjfZjo6OZvHixUyfPh0bGxsaGxs5dOgQ48eP\nB2DJkiUsXbq01wMVQgghhBhK2tq1nLpQTOyJ3K5+1pZmRiya6kv0BC88XQb2KHZ3GamVXS0FYTjQ\n0RO8qq6ZrMJfjIAX1pKcVUFSZkXXsWqVAg+nzjIUt6s9wa0tjHs8Tr3J9p/+9CcOHTpEfHw8JSUl\nWFhY8PTTTzN79mygY9GboKCgHg9MCCGEEGIoKiq/3DWKXXu5FYBgXwfmTvRiUpgbxoN8FLs7FAoF\nDjZmONiYMW6US9f2ppb2zsmYVxfmySmuI6e47prjHW1M8e5cmt7XzYae6IOiN9lWKBRMmzYNKysr\nampqmDVrFs3NzajVHYdKoi2EEEIMLK1tGr6KTeF0chk/55wnYLgdAZ62eDhZDZgOD4NNW7uGE0nF\nxJ7MJTGjYwTWytyYJdP8mDPBi+HOVgaOcGAzM1ET5G1PkLd91zaNVkdJZQNZhbVXe4IX1nLmUiln\nLpUC8G+rPG72lLdMb7KdnJzM2rVrsbe3p7q6mlmzZvHKK68QFRXFfffd1+0AhBBCCNF3sotqeX1T\nPHkl9QDklecAOUDH0t2+7rYEDLclsDMBH0or/RlCQVk9sSdzOXA6n/rGjlHsUD9Hoid6ERXqKqPY\nvUjV2dfbfZglU8a4d22vvdzSlXxDbbfPozfZfvnll9m4cSPh4eHMmzcPgFdeeYU1a9ZIsi2EEEIM\nEFqtjp1HMvli9yXaNVoWTPYhxLUFJ3d/0vNrSM+vJj2/hou/WmjEytyYgOG2Vz887bC3HtiLjBha\na5uGuKRiYk/mkJzZca2tLYxZOt2fORO9cB9maeAIhzYbSxPGBDoxJtCJ+Pj4bj+f3mS7paWF8PBw\ngK53tvb29tKBRAghhBggyqubePvrBBIzKrC1MuH5+8MZO9KZ+Pj4X/Q59gE6alszC2o6E/COJDwh\ntYyE1Ks9jh1sTAkYbov/cNuOEpThtliZ9/zEssEmv7RjFPvgmTzqG9sAGB3gSPREbyaGuGCkllHs\nwUhvsu3k5MR33313TceR2NhYHB0df+MoIYQQQvQHR88W8v6352loamNCsAvPrhiDjeXNV302M1ET\n4udIiN/Vv/N1Da1k/GL0Oz2/mpPJJZxMLunax9XBonPkuyMB93O36fWlwQeCljYNcYlFxJ7M7bpj\nYGtpwrK7O0ax3Rz7zyi2tr2doh3f0xp3gou7Y1GoVJ0fShQq9S8+V93Cx5VjOvdXqlCoVTf4XIlC\nrf7V58qOfVSd+133eed+SiUolf2+zEnvb8G//du/sXbtWl599VUaGxuJiorCxcWFN954oy/iE0II\nIcQdaGhq48PtiRyKL8DEWMUzy8cwZ4LnHSUm1hbGRAQ5XbPUdmVtE2l5HYl3Ruco+JFzhRw5VwiA\nUgHDna26Jl8GDLfF29Wmz3obG1puSR17T+Zy8Ew+l5s6RrHHBA5j7kRvxge79Lvr0FhQSPrb73A5\nPQOAagPHcztuOeG/5vMb74dShVJ99XMmTeh2fHqTbT8/P2JiYsjKyqKurg4nJyfc3d31HSaEEEII\nA0nOrODNzQmUVzcR6GnLhlWRuPVwHbCDjRlRoWZEhboCHf2NSyobfzH6XUNmQQ25JfXsP50HgFql\nxMfNurP+e/B1QGlubScusYiYE7lcyqkCwNbKhOUzA5g93gtXRwsDR3g9nU5HSUwsOZ/9N9rWVoZN\nn0Zd5BjGjB0HWg06jQadRotO0/6rz7WdX9/s49f73cIxWi269s79tBp07Ve23+zzzudr79x+g+fU\ntrWia75xzOh0eq+PaV8k2/X19ezdu5eysrLr6rSfeeaZbgcghBBCiJ7R1q7lq9gUvv0pHQWwcs4I\nVswKRK3q/VFUheLqMttTwzvapWm0OgpK60nPryatMwG/usR2DgCmxir8PH4xAXO4HS4OA6sDSk5x\nHbEncvgpPp+G5nYUCogY4UT0RC/GB7v0yfW/E63V1WS8+wHV8QmoLS0JeOFZHCdPIj4+HrW5maHD\n63VdyfpvvEG4WFys/4n00JtsP/bYY2g0Gvz9/VGppHBfCCGE6I/yS+t5fVM8WYW1uDiYs2FV5DU9\nhQ1BpVTg5WqNl6s1s8Z7AR39pLOL6q7pgHLpug4oRvh7dHQ+uZKEO9j0r+SvuaWdY+cLiTmZS2pu\nR9GFvbUJC+7yZfZ4T1wc+t8o9i9VnjxFxvsf0l5Xh+2Y0fg/9zQmDg6GDqtPKZTKjrpvI6Ob79QX\nyXZlZSX79u3r9omEEEII0fN0Oh27j2fz2Q8XaG3XMnu8J48uDsHc9DcSCAMyUqt+swPKlfrvs2nl\nnE0r7zrO3tr0mgmYhuqAkl1US8yJHA4lFNDYOYo9dqQzcyZ4MW6Uc78dxb6ivbGJ7E8+o+zAQZTG\nxvg89gdc58/tSDpFr9CbbE+ZMoUzZ84wduzYvohHCCGEELeouq6ZjVvOEp9ShpW5ERtWRzIpzM3Q\nYd22G3VAqW9svTr6ndeRgJ+6UMKpC33fAaWppZ2j5wqJPZlDWl4N0NH+cNEUP2aP98TJ3rzHz9kb\n6i6lkPbWRlpKy7Dw9SFw3fOYew43dFiDnt6fyKioKB577DFMTU0xN7/2h+nAgQO9FpgQQgghbu5k\ncjHvbj1HXUMr4YHDeP6B8H5XatEdVubGRIxwImLEtR1Quvp/51X/ZgcU/87yEx836zvuX51ZUEPs\nyVwOJRTQ1NKOUgHjRjkzd6I3kUFOqPr5KPYV2vZ28r/eSsG320Gnw+O+pQx/YAXK3yqfED1Gb7L9\n7//+77z44osEBgailFsMQgghhEE1tbTz6ffJxJ7MxUit5PEloSyY7INykHT0+C0ONmY42JgxMeT2\nOqB4d3ZACeycgOnhfPMOKI3NbRw911GLnZHfMYrtaGPKvdP8mDXei2F2A+sNTWNBAWlvvkNDZiYm\nTk4ErnsO61EjDR3WkHJLi9qsXr26L2IRQgghxG9Iza3ija8SKK5owMfNmg2rI/FysTZ0WAZzqx1Q\ncopqycivYU/ncTfqgFJY2cqJbec4craAphYNSgVMCHYheqIXEUHOA649oU6no2R3DDmff4G2tRWn\nGXfj89jvUZsPjJKXwURvsr106VL+8pe/MGvWLCwsrp1ZGxER0WuBCSGEEKKDRqNl64F0vt6Xik6n\nY9nd/qyeGyTLe9/AzTqg5BR3dkDpXIjn1x1QrhhmZ8bSu72YPd5zwJbltFRWkfHu+9ScPYfayorA\n9c/jEDXR0GENWXqT7c8++wyAo0ePXrNdoVBIzbYQQgjRy4orGnjjq3hSc6txtDVj/coIQv0d9R8o\nuhipVZ0dTOxgUse2ppZ2sgpruyZgVlVXsWz2aMJHOA24Uexfqog7QeYHH9JefxnbiHACnn0aY3s7\nQ4c1pOlNtg8ePNgXcQghhBDiF3Q6Hft/zuPjnUk0tWiYOsadp5aFYWmAdneDkZmJmmBfB4J9O3pL\nx8fHEznS2cBR3bn2xkayP/6UsoOHUBob4/v4o7jMnzugFgcarPQm2zqdjl27dnH8+HEqKytxdHRk\n+vTpREdH90V8QgghxJBTe7mF9785z4mkYsxN1WxYHcn0CA9DhyX6qdoLF0l/+11aysqw8PMjcP1z\nmHvIz0t/oTfZfu211zhz5gwLFy7E2tqampoaPvroI9LT02W5diGEEKKHJaSWsfHrBKrqWgj2dWD9\nyogB08dZ9C1tWxt5m7dQ+N0OUCjwWL6M4fcvl5Z+/YzeZPvIkSN89913mJiYdG1bsWIFy5cvl2Rb\nCCGE6CEtbRr++8eL/HA0C7VKwSMLRrFkuv+Arh8WvacxL5+0tzbSkJWNqYszAS88h/XIIEOHJW5A\nb7Kt0WgwNr62PszU1BStVttrQQkhhBBDSVZhLa9viie/tJ7hzpZsWBWJn4etocMS/ZBOq6X4xz3k\nfvFlR0u/WTPw+cPvUZsPzM4pQ4HeZHvChAk89dRTrFixoquM5JtvvmHiRGkhI4QQQnSHVqtjx+EM\n/rXnEu0aHfdM9uGRhcGYGElLP3G9lspKMt55n5pz51FbWxO44QUcJk4wdFhCD73J9iuvvMLnn3/O\np59+SlVVVdcEyYceeqgv4hNCCCEGpfLqJt7anEBSZgV2ViY8d384YwdwNwzRuyqOx5H5wUe0X76M\nXWQ4/s8+jbGdtPQbCPQm28bGxjz++OM8/PDD1NXVYWNjc11ZiRBCCCFu3ZGzBXzwzXkamtuZGOLC\nM8vHYGNpov9AMeS0NzSQ9Y9PKT90uKOl35OP4TI3Wlr6DSB6k+3ExET+8pe/kJKS0rUtJCSEv/zl\nL4SEhPRqcEIIIcRgcrmpjY++S+RQQgGmxiqeXTGG2eM9JXESN1R74UJnS79yLAP8CXjhOcw93A0d\nlrhNepPt9evX88QTTxAdHY21tTW1tbXExMTw/PPPywqSQgghxC1Kyqzgrc0JlFc3McLTjvWrI3Bz\ntDR0WKIf0ra1kffV1xRu3wkKBcPvX47HivtQqvWmbaIf0vu/plarWb58edfXNjY23H///V3LuAsh\nhBDi5tratWyKucR3hzJQKBSsnDOC+2cFolIpDR2a6Ica8/JIe3MjDdk5mLq4ELj+eaxGBBo6LNEN\nepPtu+++m5iYGObOndu17cCBA8ycObNXAxNCCCEGuvzSel7/Mp6solpcHSxYvyqCIG97Q4cl+iGd\nVkvxrt3kfPElurY2nGfPwucPj6Ayk5Z+A53eZPv48eN88cUX/PnPf+5q/dfc3Iybm9s1ZSSxsbG9\nGqgQQggxUOh0OnYfz+azHy7Q2q5l9nhPHl0cgrmprOwnrtdSUUn6xnepTUzCyMYav6c34DBhnKHD\nEj1Eb7L9pz/9qS/iEEIIIQaF6rpm3t5yloSUMqzMjXnxwdFEhboZOizRT5UfPU7mf32EpqEBu3GR\n+D+zFmNbWdBoMNGbbI8fP74v4hBCCCEGvBNJxby37Rx1Da1EjHDi+QfCsbc2NXRYoh9qv9xA1j8+\nofzwEZQmJvitfQLnObOlM80gJNNaxYCXllfN8Uv1jAxuk1u0QgiDaGpp55Odyew9lYuxWskT94ay\nYLKPJE7ihmqTkkl7+11aKyqwDAwgcN1zmLnJ3Y/BSpJtMWBlFNTwVWwKpy+WAnCx4AgvPTIOLxdr\nA0cmhBhKUnKreHNTAsWVDfi62bB+dYS8Dokb0ra1kfvlVxTt/KGjpd/K+xm+fBkKlcrQoYleNCCT\n7WPnC4kKdUOllBGDoSi7qJavYlM4mVwCwCgfe8xULcRnXGbDxiM8s3wM0yM8DBylEGKw02i0bN2f\nxtf709DpdCy725/Vc4MwUkviJK7XkJNL2lsbaczJxdTVhcB10tJvqBiQyfZ/fnEG92GW3DcjgOmR\nHqilV+mQkFNcx+a9KcQlFgMQ5GXH6rlBjA4YRkJCArMnj2Lj12d5Y1M8KTlV/GFRsPzRE0L0iqKK\ny7y5KYHUvGocbc1YvzKCUH9HQ4cl+iGdVkvRD7vI/WITuvZ2nKPn4PP7h1GZSi3/UDEgk+3Z4z05\neCafjVvOsnlvCkvvDmDWeE9MjCSxGozySurYvDeVY+eLAAj0tGVVdBARI5yuqYecHOaGt6s1f//8\nZ348nk1Gfg3/c804htlJj1IhRM/Q6XTs+zmPj3ck0dyqYVq4B08uC8PSTOaLiOu1lFeQ/s57nS39\nbPB/di3248YaOizRxwZksv3c/eE8MGcE2w9lsPdkLh9+l8jX+1K5d5ofc6O8ZZLcIJFfWs/X+1I5\neq4QnQ78PWxYFR3E2JHON5105D7Mktefm8r7357nUHwBz795iBcfjCRihFMfRy+EGGxqL7fw3rZz\nnEwuwcJUzYbVkVKyJm6q/MhRMj/8GE1DA/bjx+H39FMY29oYOixhAAMy2QZwsjPniXvDWDErkJ2H\nM9kdl8M/d11k24F0Fk3x5Z4pvliZGxs6THEHisovs3lfKkcSCtDqwNfNhlXRIxgf7HJLM/tNTdSs\nXxnBKG97/rEjmX/7+ASrooNYMTMQpdT5CyHuQEJKGW9/nUB1fQshfg6sWxmBk525ocMS/VD75ctk\nfvQxFUeOoTQ1xe/pp3CePVM60wxhAzbZvsLOypRH7gnmvhkB7DqezfdHMvlqbyrbD2cwL8qHJdP8\nsJMepwNCSWUDX+9L5af4ArRaHd6u1qyKHsGEYNfbTpIVCgXzJvng52HLq1+cZlNMCik5VaxfFYm1\nhbwJE0LcmpY2DZ/vusCuY9moVQp+d88oFk/zlwn64oZqEpNIf/tdWisrsRoRSMC65zBzdTV0WMLA\nBnyyfYWluTEPzB7B4ql+xJ7MYfuhDL47lMGuY1nMnuDF0un+ONnLKER/VFrVyJZ9qRw4k49Wq8PT\nxYpVc4KICr39JPvXAj3teHvddN7YFE98Shnr3jrE/3p4HAHD7XooeiHEYJVZUMMbX8WTX3qZ4c6W\nvLh6LL7uUgYgrqdtbSX3X5so+n4XKJV4rnoAj/uWSks/AfRhst3e3s7rr7/O559/zuHDh3F2dgbg\n9ddfZ//+/SiVSmbNmsX69eu7dR4zEzVLpvkzf5IPB07n8c1PGfx4PJuYEzlMj/TgvhkBeDhZ9cB3\nJLqrrLqRrfvT2P9zHhqtDg8nS1bNCWLyaLceLfewtjDmz49OZOu+VDbvS+WP7x7j8XtDmTvRS27r\nCSGuo9Hq2HEogy9jLtGu0XHPXT48ck+wTMIXN9SQk0PamxtpzM3D1M2NwPXPYxXgb+iwRD/SZ8n2\n2rVrCQsLuya5+fHHHzlz5gy7du1Cp9Px0EMPsXfvXubMmdPt8xkbqZg3yYfZE7w4craQbw6mceB0\nPgfP5DM5zI0VswLxcZMRCkOoqGli64E09p3KpV2jw32YBQ/MHsGUcI9euzWrUipYGR3ECC97Xt90\nhg++OU9KThVPLQvD1HjQ3OARQnRTWXUjb21OIDmzEjsrE55/IJzIIGdDhyX6IZ1WS9HOH8j98it0\n7e24zIvG+5E10tJPXKfPsoynn36a0aNH895773Vti42N5d5770Wt7ghj0aJFxMTE9EiyfYVapWTG\n2OFMj/DgRHIxW/encex8EcfOFzF2pDP3zwokyNu+x84nbq6ytolvDqYTcyKXdo0WVwcLHpgTyLRw\nD1R91Cs9IsiJt9dN59UvTnPwTD5ZhbW89PA43IZZ9sn5hRD916GEAj789jwNze1MDHHhmeVjsLE0\nMXRYoh9qKS8n7e13qUu+gJGtbUdLv7GRhg5L9FN9lmyPHj36um3Z2dmsXLmy62tPT0+2bt3aK+dX\nKhVMDnNjUqgrCallbN2fxplLpZy5VEqYvyMrZgYSFuAoZQW9oLqumW9+SicmLofWdi3O9uY8MDuQ\nuyOH91mS/UtO9ub85zN38cnOZHbH5bDu7cO88EA4UaFufR6LEMLwLje18V/fnufI2UJMjVU8t2IM\ns8Z7yt8DcR2dTkf54aNk/eNjNA2N2E8Yj//TT2JkI3fKxc0Z9P55c3MzxsZXO0OYmprS1NTUq+dU\nKBREBjkTGeRMcmYF2w6kk5BaRmJGBYGetqyYGci4US7SIq4H1NS38O1P6eyOy6G1TcMwOzPunzWC\nmeOGG3zVTyO1iqeWjSbI2573tp3nPz4/zdLp/qyZP9IgbwCEEIaRlFHBm5sTqKhpYoSXHRtWReLq\naGHosEQ/1FZfT9aHH1Nx7DhKU1P8n12L08wZ8qZM6KXQ6XS6vjxhUFBQ1wTJRYsW8dJLLxEVFQXA\n0aNHefPNN9m+fftNj4+Pj+/xmAorWzl6oY6UgmYAnGyNmDLKimBPM0m670BDs4a4S/X8nNZAm0aH\ntbmKqcFWjPG1QK3qf9eztKaNrUcrqaxvx8vJmPsmO2BlJhOhhBjM2jU6DibWEnfpMgoFTAuxZkqw\nlbT0EzekycqmbecuqK9H4eGB0b0LUdpJV6uhIjKyeyVCBhnZvvIu0NfXl9zc3K5kOzc3Fz8/P73H\nd/ebvu75gEVzILekjm8OpnPkbCHfxlURl2bBfTMCuDtyOEbq/jfaGR8f3+PXojvqG1vZ3tlusalF\ng721KStmBTJngidG6t5NXrt7LaZPbmPjlrPEJRbz2f4q/vjQWEL8HHswwr7T334uDEmuxVVyLa7a\nc/AkMWebySq6jKujBRtWRTDCa2jO3ZGfi6tudC00LS3k/msTxT/8iEKlYvjqlXgsu3fQt/STn4ur\nemKQ1yDJ9pXB9Hnz5vHRRx+xePFitFotW7ZsYcOGDYYICQAvF2s2rIpkdXQQ3xxM58DpfN7deo7N\nsSnce7c/cyZ4SeeKG7jc2MqOI5l8fySLppZ27KxMeHDeSOZO9MZ4gLTKMjc14n+tGcfOI5n8c9dF\nXvkwjofnj+Le6X5yi1CIAUyr1VFe00ReSR35pfXkltRz5Gwp7RqYM8GLRxeHYGYir+viepezskl7\n822a8gsw83AncN3zWPrrHxAU4tf65BWmsrKSBx98EOgY1V6zZg0qlYrPP/+cKVOmsGTJEhQKBQsX\nLmT69Ol9EdJvcnGw4JnlY1g5ZwTbD2USczKHj3cks3V/Goun+rFgsg/mpkaGDtPgGpra+P5IJjuP\nZNLQ3I6tpQmrooOYN8l7QPajVSgULJnmT8BwO17712n+uesCKblVPH9/OBZm8v8tRH+m1eooq24k\nv7SevJJ68ko7PgpK62lu1Vyzr4Wpkj8+NJaoUFnZT1xPp9FQuPMH8jZt7mjpN39uR0s/E+lMI+5M\nnyTbDg4O7Nmz54aPrVu3jnXr1vVFGLfNwcaMRxeHsHxmAN8fzeLHY1l8sfsS3x5M5567fFk4xXdI\ntoVqbG7jh6NZbD+cSUNTG9YWxvzunmDmT/LGdBCMEAX7OvD2uum89uUZTiQVk1Ncx0vgJtt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cnlklBc2SiH658K69Biscvbk2JC5RMaz86M5v9HP7NUVODQyqdgraxC3OxfIPPOO3hVSCIaVBi2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\nOs6oBvB0+AV50TMa7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u3bh7feegvvvfce1q9fj4SEBLzwwgvyYzZt2oSXX34ZW7ZsQV1d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\nCMM2EREREVEfYdgmIiIiIuoj/x+dzF+WpLoW+AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f314205af50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "evaluate_models(10, 50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sparse Graph with Discrete Emissions\n",
    "\n",
    "Lets also compare MultinomialHMM to a pomegranate HMM with discrete emisisons for completeness."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def initialize_components(n_components, n_seqs):\n",
    "    \"\"\"\n",
    "    Initialize a transition matrix for a model with a fixed number of components,\n",
    "    for Gaussian emissions with a certain number of dimensions, and a data set\n",
    "    with a certain number of sequences.\n",
    "    \"\"\"\n",
    "    \n",
    "    transmat = numpy.zeros((n_components, n_components))\n",
    "    transmat[-1, -1] = 1\n",
    "    for i in range(n_components-1):\n",
    "        transmat[i, i] = 1\n",
    "        transmat[i, i+1] = 1\n",
    "    transmat[ transmat < 0 ] = 0\n",
    "    transmat = (transmat.T / transmat.sum( axis=1 )).T\n",
    "    \n",
    "    start_probs = numpy.abs( numpy.random.randn(n_components) )\n",
    "    start_probs /= start_probs.sum()\n",
    "\n",
    "    dists = numpy.abs(numpy.random.randn(n_components, 4))\n",
    "    dists = (dists.T / dists.T.sum(axis=0)).T\n",
    "    \n",
    "    seqs = numpy.random.randint(0, 4, (n_seqs, n_components*2, 1))\n",
    "    return transmat, start_probs, dists, seqs\n",
    "\n",
    "def hmmlearn_model(transmat, start_probs, dists):\n",
    "    \"\"\"Return a hmmlearn model.\"\"\"\n",
    "\n",
    "    model = MultinomialHMM(n_components=transmat.shape[0], n_iter=1, tol=1e-8)\n",
    "    model.startprob_ = start_probs\n",
    "    model.transmat_ = transmat\n",
    "    model.emissionprob_ = dists\n",
    "    return model\n",
    "\n",
    "def pomegranate_model(transmat, start_probs, dists):\n",
    "    \"\"\"Return a pomegranate model.\"\"\"\n",
    "    \n",
    "    states = [ DiscreteDistribution({ 'A': d[0],\n",
    "                                      'C': d[1],\n",
    "                                      'G': d[2], \n",
    "                                      'T': d[3] }) for d in dists ]\n",
    "    model = HiddenMarkovModel.from_matrix(transmat, states, start_probs, merge='None')\n",
    "    return model\n",
    "\n",
    "def evaluate_models(n_seqs):\n",
    "    hllp, plp = [], []\n",
    "    hlv, pv = [], []\n",
    "    hlm, pm = [], []\n",
    "    hls, ps = [], []\n",
    "    hlt, pt = [], []\n",
    "\n",
    "    dna = 'ACGT'\n",
    "    \n",
    "    for i in range(10, 112, 10):\n",
    "        transmat, start_probs, dists, seqs = initialize_components(i, n_seqs)\n",
    "        model = hmmlearn_model(transmat, start_probs, dists)\n",
    "\n",
    "        tic = time.time()\n",
    "        for seq in seqs:\n",
    "            model.score(seq)\n",
    "        hllp.append( time.time() - tic )\n",
    "\n",
    "        tic = time.time()\n",
    "        for seq in seqs:\n",
    "            model.predict(seq)\n",
    "        hlv.append( time.time() - tic )\n",
    "\n",
    "        tic = time.time()\n",
    "        for seq in seqs:\n",
    "            model.predict_proba(seq)\n",
    "        hlm.append( time.time() - tic )    \n",
    "        \n",
    "        tic = time.time()\n",
    "        model.fit(seqs.reshape(n_seqs*i*2, 1), lengths=[i*2]*n_seqs)\n",
    "        hlt.append( time.time() - tic )\n",
    "\n",
    "        model = pomegranate_model(transmat, start_probs, dists)\n",
    "        seqs = [[dna[i] for i in seq] for seq in seqs]\n",
    "\n",
    "        tic = time.time()\n",
    "        for seq in seqs:\n",
    "            model.log_probability(seq)\n",
    "        plp.append( time.time() - tic )\n",
    "\n",
    "        tic = time.time()\n",
    "        for seq in seqs:\n",
    "            model.predict(seq)\n",
    "        pv.append( time.time() - tic )\n",
    "\n",
    "        tic = time.time()\n",
    "        for seq in seqs:\n",
    "            model.predict_proba(seq)\n",
    "        pm.append( time.time() - tic )    \n",
    "        \n",
    "        tic = time.time()\n",
    "        model.fit(seqs, max_iterations=1, verbose=False)\n",
    "        pt.append( time.time() - tic )\n",
    "\n",
    "    plt.figure( figsize=(12, 8))\n",
    "    plt.xlabel(\"# Components\", fontsize=12 )\n",
    "    plt.ylabel(\"pomegranate is x times faster\", fontsize=12 )\n",
    "    plt.plot( numpy.array(hllp) / numpy.array(plp), label=\"Log Probability\")\n",
    "    plt.plot( numpy.array(hlv) / numpy.array(pv), label=\"Viterbi\")\n",
    "    plt.plot( numpy.array(hlm) / numpy.array(pm), label=\"Maximum A Posteriori\")\n",
    "    plt.plot( numpy.array(hlt) / numpy.array(pt), label=\"Training\")\n",
    "    plt.xticks( xrange(11), xrange(10, 112, 10), fontsize=12 )\n",
    "    plt.yticks( fontsize=12 )\n",
    "    plt.legend( fontsize=12 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jmschr/anaconda/lib/python2.7/site-packages/ipykernel/__main__.py:77: DeprecationWarning: converting an array with ndim > 0 to an index will result in an error in the future\n"
     ]
    },
    {
     "data": {
      "image/png": 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AVxJTGTd9G+evXKd3+5o806u+9mYXAoVtERERkRImNj6FcZ9v42JcCo92eogn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\nAIA5qSF4eG0mkmMC3FwZ0fQjiiJOFVRj76dFsNsEzF+WiJV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6ZDBYM1QTEU17Exa2bTYb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\nOAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3142133a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "evaluate_models(50)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
